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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On sampling theory associated with the resolvents of singular Sturm-Liouville problems


Author: M. H. Annaby
Journal: Proc. Amer. Math. Soc. 131 (2003), 1803-1812
MSC (2000): Primary 41A05, 34B05, 94A20
Published electronically: October 2, 2002
MathSciNet review: 1955268
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Abstract: This paper is concerned with the sampling theory associated with resolvents of eigenvalue problems. We introduce sampling representations for integral transforms whose kernels are Green's functions of singular Sturm-Liouville problems provided that the singular points are in the limit-circle situation, extending the results obtained in the regular problems.


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Additional Information

M. H. Annaby
Affiliation: Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt
Address at time of publication: Department of Mathematics, Arizona State University, P.O. Box 871804, Tempe, Arizona 85287-1804
Email: mnaby@math-sci.cairo.eun.eg, annaby@math.la.asu.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06727-8
PII: S 0002-9939(02)06727-8
Keywords: Sampling theory, singular Sturm-Liouville problems, Green's function, resolvent kernels, Legendre and Bessel functions
Received by editor(s): November 15, 2000
Received by editor(s) in revised form: January 18, 2002
Published electronically: October 2, 2002
Communicated by: Carmen C. Chicone
Article copyright: © Copyright 2002 American Mathematical Society